Question: Simplify the following expression: $ r = \dfrac{1}{8} - \dfrac{6t + 4}{7t} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7t}{7t}$ $ \dfrac{1}{8} \times \dfrac{7t}{7t} = \dfrac{7t}{56t} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{6t + 4}{7t} \times \dfrac{8}{8} = \dfrac{48t + 32}{56t} $ Therefore $ r = \dfrac{7t}{56t} - \dfrac{48t + 32}{56t} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{7t - (48t + 32) }{56t} $ Distribute the negative sign: $r = \dfrac{7t - 48t - 32}{56t}$ $r = \dfrac{-41t - 32}{56t}$